# Did ISEE-3 spend a few years in a halo orbit around sun-earth $L_1$ without using any fuel?

In a related question I'm trying to find some conclusive reference(s) helping explain if some halo orbits around the sun-earth or earth-moon $L_1$ or $L_2$ locations can actually be somewhat stable (say, for half-a-dozen orbits). There I mentioned the quote by Dennis Wingo describing ISEE-3's original Halo orbit. He describes Sun-Earth $L_1$ as "a point about 1.5 million kilometers from earth where a spacecraft can safely orbit without using any fuel."

The site http://spacecraftforall.com/a-new-orbit is an interactive thing - if you leave it alone it will usually start the video in about 10 or 15 seconds.

Here I would just like to know specifically - did ISEE-3 spend a few years in a halo orbit around sun-earth $L_1$ without using any fuel, or at least without the regular station keeping thrust maneuvers needed in unstable orbits? (e.g. like DSCOVR needs to do)

• Thanks for your help! I got started on this with the linked sibling question which cites a JAXA patent stating that the stable halo orbits around $L_1$ are too large for some applications, here you are suggesting they are too small. Is there a "Goldilocks Zone" for halo orbits? I could really use a reference or two - even if it's behind a paywall I can start there and find something that can be linked-to here. – uhoh May 20 '16 at 0:48
• @HopDavid these are orbits around $L_1$ (or $L_2$). Remember the saddles and dimples we talk about in 2D and 3D have to be calculated for a single - and usually zero - velocity. The "potential" in the rotating frame is a pseudo-potential and includes velocity terms. It's why every explanation that uses those plots always ahem's and guffaws when it gets to $L_4$ and $L_5$, which for sun-earth and earth-moon are stable and yet the plots show a maximum which then is explained away by saying this isn't actually the correct plot to look at anyway. Need a way to see potential in 6 dimensions! – uhoh May 20 '16 at 13:36